- #31
mathdad
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Ok. Great. Let us move on. I will post similar word problems in the coming days.
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SUMMARY
The discussion centers on the physics of two balls thrown vertically upward from different heights and initial speeds, specifically analyzing which ball hits the ground first. The first ball is thrown from a height of 50 feet with an initial speed of 40 ft/sec, while the second ball is thrown from 100 feet with an initial speed of 5 ft/sec. The height of each ball over time is described by the equation h(t) = -16t² + v₀t + h₀. To determine the time of impact for each ball, the quadratic formula is applied, leading to the conclusion that the ball with the smaller time value will hit the ground first.
PREREQUISITES- Understanding of kinematic equations in physics
- Familiarity with the quadratic formula
- Knowledge of gravitational acceleration (32 ft/s²)
- Basic algebra skills for solving equations
- Study the derivation and application of the quadratic formula in kinematics
- Explore the effects of air resistance on projectile motion
- Learn about the differences in equations for objects thrown downward versus upward
- Investigate more complex models of motion involving varying gravitational forces
Students of physics, educators teaching kinematics, and anyone interested in understanding the principles of projectile motion and the application of quadratic equations in real-world scenarios.
- #32
MarkFL
Gold Member
MHB
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Okay, so we've found:
$$t=\frac{v_0\pm\sqrt{v_0^2-2a\Delta x}}{a}$$
Suppose we have $\Delta x=0$. At what times does that occur?
$$t=\frac{v_0\pm\sqrt{v_0^2-2a\Delta x}}{a}$$
Suppose we have $\Delta x=0$. At what times does that occur?
- #33
mathdad
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MarkFL said:
Replace (delta)x with 0 and simplify, right?
- #34
MarkFL
Gold Member
MHB
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RTCNTC said:
Yes. :)
- #35
mathdad
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Thank you for all your help.
- #36
MarkFL
Gold Member
MHB
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Um, okay.
I was attempting to share with you some of the ways I used to go about learning things that helped me succeed in my math studies, but if you just wish to walk away from that, then so be it. Examining formulas at the boundaries of the parameter values gave me a good number of "aha" moments. Looking at how one values changes in relation to another is also illuminating.
I was attempting to share with you some of the ways I used to go about learning things that helped me succeed in my math studies, but if you just wish to walk away from that, then so be it. Examining formulas at the boundaries of the parameter values gave me a good number of "aha" moments. Looking at how one values changes in relation to another is also illuminating.
- #37
mathdad
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MarkFL said:
I thank you for helping me as I march on my way to succeed with word problems.
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